I was investigating the LU Decomposition essay on the J wiki (
http://www.jsoftware.com/jwiki/Essays/LU%20Decomposition )

The verb presented there seems to fail (index error) for singular matricies.
  LU 1 1 1 , 2 2 2 ,: 3 3 3
|index error: LU
|   p;(=1);p    {"1 A[p=.C.(n-1);~.0,(0~:,A)i.1

My understanding is that LU decomposition should work with any square
matrix (singular or not).
Is this a known downside of this particular algorithm?
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